The theoretical part presents the settings of numerical modeling required for the simulation of orthogonal cutting. After explaining what the Finite Element Method is, a description of FEM formulations is given and friction models, material models, types of integration and the method of network regeneration are studied. In the further theoretical part, the concept of orthogonal cutting, input and output cutting parameters are explained. In order to clarify the importance of this graduate thesis, a review of scientific research in the field of numerical modeling of orthogonal cutting is given. Before the practical part, the division of aluminum alloys and the machinability of each series are stated. In the practical part at the Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, an orthogonal cutting experiment was performed on an aluminum pipe realized by turning. This work presents the required tools, machine tool, machining parameters and experimental results in the form of cutting forces. Then, in the Design Expert software package, an experimental plan was created that gave a series of experiments with different finite element sizes. Based on the experiment plan, the results of the orthogonal cutting simulation were obtained. The calculation of the cutting force error followed and a mathematical model was obtained in the Design Expert. The duration of the simulation is also included. At the end, the optimization of the mathematical model of the error and time dependence on the network size in the Matlab software package was performed. The optimization was performed by a genetic algorithm and the optimal result is given.